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系統識別號 U0026-0601202019350400
論文名稱(中文) 嵌入式多層石墨烯奈米結構系統之三維非局部彈性力學靜力分析
論文名稱(英文) Static Analysis of Embedded Multiple Graphene Sheet Systems Based on the Three-dimensional Nonlocal Elasticity Theory
校院名稱 成功大學
系所名稱(中) 土木工程學系
系所名稱(英) Department of Civil Engineering
學年度 108
學期 1
出版年 108
研究生(中文) 林稚宸
研究生(英文) Chih-Chen Lin
學號 N66074108
學位類別 碩士
語文別 中文
論文頁數 45頁
口試委員 指導教授-吳致平
口試委員-徐德修
口試委員-王永明
口試委員-方中
口試委員-蘇于琪
中文關鍵字 Eringen非局部彈性力學理論  Winkler模型  多層石墨烯薄板系統  非局部平面應變彈性理論  微擾方法  靜態分析 
英文關鍵字 Eringen’s nonlocal elasticity theory  foundation  multiple graphene sheet systems  nonlocal plane strain elasticity theory  static  the perturbation method 
學科別分類
中文摘要 本文推衍漸近非局部平面應變理論,將其用於具簡支承邊界的多層石墨烯薄板系統承載圓柱形彎曲(Cylindrical Bending)載重下之撓曲分析,文中考慮此奈米結構係置放於彈性介質上。其中多層石墨烯薄板系統(Multiple Graphene Sheet System, MGSS)在y方向上的尺寸遠大於在x及z方向上的尺寸,使得所有場變量皆可認定獨立於y座標。本文利用Eringen非局部理論關係將多層石墨烯薄板系統靜態行為公式中的微小尺度效應納入本分析中。而多層石墨烯板與其周圍環境彈性介質及相鄰兩石墨烯板彼此間的相互作用均以不同勁度係數的單參數Wrinkler彈性支承模擬,前者利用參數kw表示,後者則是利用參數cw表示。演算過程中利用非局部參數導入微小尺度效應於彈性材料之組成方程式,應用無因次化、漸近展開及連續積分之數學運算過程於獨立單層石墨烯板,再將各層石墨烯板之運動方程式組合成多層石墨烯薄板系統,形成一套遞迴循環的各階問題之系統控制方程式。文中亦針對此多層石墨烯薄板系統的靜態行為進行參數研究,考慮之係數有:縱橫比、石墨烯薄板的數量、相鄰層間介質的勁度與周圍介質的勁度、石墨烯板之厚長比與非局部參數。
英文摘要 An asymptotic local plane strain elasticity theory is reformulated for the static analysis of a simply-supported, multiple graphene sheet system (MGSS) in cylindrical bending and resting on an elastic medium, in which the dimension of the MGSS in the y direction is much greater than those in the x and z directions, such that all the field variables are considered to be independent of the y coordinate. Eringen’s nonlocal constitutive relations are used to account for the small length scale effects in the formulation examining the static behavior of the MGSS. The interaction between the MGSS and its surrounding foundation is modelled as a Winkler foundation with the parameter kw, and the interaction between adjacent graphene sheets (GSs) is considered using another Winkler model with the parameter cw. A parametric study with regard to some effects on the static behavior of the MGSS resting on an elastic medium is undertaken, such as the aspect ratio, the number of the GSs, the stiffness of the medium between adjacent layers and that of the surrounding medium of the MGSS, and the nonlocal parameter.
論文目次 目錄

摘要 I
Extended Abstract II
誌謝 VI
目錄 VII
表目錄 VIII
圖目錄 IX
第一章 緒論 1
第二章 漸近式非局部平面應變彈性理論 4
2.1 非局部彈性力學理論之基本方程式 4
2.2 無因次化 6
2.3 漸近展開 7
2.4 各階問題之控制方程組 9
2.4.1 ∈^0階問題 9
2.4.2 ∈^2k階問題 11
第三章 應用微擾方法於奈米石墨烯板之非局部撓曲行為分析 14
3.1 ∈^0階解 14
3.2 ∈^2k階修正解 16
第四章 數值範例 18
4.1 單層正向性巨觀板 18
4.2 多層石墨烯薄板系統 19
第五章 結論 21
第六章 參考文獻 22

表目錄

表 1 具完全簡支承邊界的正向性單層板承受圓柱形彎曲正弦分佈載重下各場變量於特定點位上之漸近解。 26
表 2 具完全簡支承邊界的單層、雙層及三層石墨烯薄板系統於板的頂面承受圓柱形彎曲正弦分佈載重下各場變量於特定點位上之 階收斂解。 27

圖目錄

圖 1 石墨烯材料結構示意圖 29
圖 2 三層石墨烯薄板系統剖面圖及Winkler模型描述層與層之間中平面相互作用行為和其彈性基礎示意圖 30
圖 3 具完全簡支承邊界的無限長正交性厚板的上表面承受正弦分佈載重,各階漸近問題之各場變量沿厚度方向之分佈 31
圖 4 三層石墨烯薄板系統的各場變量在不同非局部參數下沿厚度方向之分佈 32
圖 5 三層石墨烯薄板系統的各場變量在不同基礎勁度參數下沿厚度方向之分佈 33
圖 6 三層石墨烯薄板系統的各場變量在不同層間Winkler參數下沿厚度方向之分佈 34

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